MathDB

A regular spatial pentagon consists of five points

P_1,P_2,P_3,P_4

and

P_5

\mathbb{R}^3

such that

|P_iP_{i+1}|=|P_jP_{j+1}|

and

\angle P_{i-1}P_iP_{i+1}=\angle P_{j-1}P_jP_{j+1}

for all

1\leq i,\leq 5

, where

P_0=P_5

and

P_{6}=P_{1}

. A regular spatial pentagon is planar if there is a plane passing through all five points

P_1,P_2,P_3,P_4

and

P_5

.
Show that every regular spatial pentagon is planar.

Problem Statement